Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds
Differential Geometry
2019-08-13 v2
Abstract
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.
Keywords
Cite
@article{arxiv.1602.07824,
title = {Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds},
author = {Songbo Hou},
journal= {arXiv preprint arXiv:1602.07824},
year = {2019}
}
Comments
20 pages